PROPER AND ISOLATED EFFICIENCIES IN MULTIOBJECTIVE OPTIMIZATION PROBLEMS
Keywords:Optimality condition, Duality, Isolated minimizer, Mordukhovich sub-differential, L-invex-infine function, Multi-objective optimisation
We employ some advanced tools of variational analysis and generalised differentiation such as the nonsmooth version of Fermat's rule, the limiting sub-differential of maximum functions, and the sum rules for the Frechet and Mordukhovich sub-differentials to establish necessary conditions for (local) properly efficient solutions and (local) isolated minimizers of a multi-objective optimisation problem involving inequality and equality constraints. Sufficient conditions for the existence of such solutions are also supplied under assumptions of (local) convex/affine functions or L-invex-infine functions defined in terms of the limiting sub-differential of locally Lipschitz functions. In addition, we propose a type of Wolfe dual problem and explore weak/strong duality relations under L-invexity-infineness hypotheses.
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Copyright (c) 2012 Thái Doãn Chương
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